Na, Trump's aim isn't to break NATO. The US needs NATO as much as Europe needs it too. One thing that has bi-partisan support in the US is that they consider most NATO allies as "free riders" (as Obama called them) for not investing and upgrading their military. The western superpowers want NATO to abandon its defensive objectives, and become more offensive, to be more pro-active as a "world police", to "pay their dues". Threats to annex Greenland is just posturing to convey a strong message to the EU members of NATO that if the US has Greenland, NATO can be shrunk (by kicking out some of these "free riders"). The implicit message to the Europeans is to increase spending and militarise, to enhance NATO war readiness, if they want to be in NATO.

Note that most Europeans are explicitly not interested in increasing spending on their military and NATO. Prolonging the Ukraine war (and sabotaging the peace efforts), and Trump's theatrics, provides an excuse for European politicians to use fear-mongering to sway their people to spend more on the military. European politicians (as do other politically experienced countries) understand that Trump will never be able to mobilise support within the US polity, within its military, to attack a European country who is their ally. (And, as I said before, he isn't a fool to even attempt so).

Worryingly, the first quarter of this century has already seen all the basic foundation for another world-war - military confrontations in Europe, Asia, the Middle-east and now in South America too, efforts to form another military alliance in Indo-Pacific front (QUAD) and realignment of economic alliances (BRICS). A systematic, brutal massacre and genocide in Gaza has also been confirmed (the embers of which still threaten to engulf the whole of middle-east). Hence, this effort by the west to militarise is concerning as it means they are planning another military confrontation soon with Russia (in the Baltics and Arctic, over its Arctic plans that threaten the maritime power of the US) and / or China. That does not bode well for any of us ...